Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators.

Knowledge beliefs and attitudes of squash venue operators relating to use of protective eyewear

Sports venues are in a position to potentially influence the safety practices of their patrons. This study examined the knowledge, beliefs and attitudes of venue operators that could influence the use of protective eyewear by squash players. A 50% random sample of all private and public squash venues affiliated with the Victorian Squash Federation in metropolitan Melbourne was selected. Face-to-face interviews were conducted with 15 squash venue operators during August 2001. Interviews were transcribed and content and thematic analyses were performed. The content of the interviews covered five topics: (1) overall injury risk perception, (2) eye injury occurrence, (3) knowledge, behaviors, attitudes and beliefs associated with protective eyewear, (4) compulsory protective eyewear and (5) availability of protective eyewear at venues. Venue operators were mainly concerned with the severe nature of eye injuries, rather than the relatively low incidence of these injuries. Some venue operators believed that players should wear any eyewear, rather than none at all, and believed that more players should use protective eyewear. Generally, they did not believe that players with higher levels of experience and expertise needed to wear protective eyewear when playing. Only six venues had at least one type of eyewear available for players to hire or borrow or to purchase. Operators expressed a desire to be informed about correct protective eyewear. Appropriate protective eyewear is not readily available at squash venues. Better-informed venue operators may be more likely to provide suitable protective eyewear.

Time-evolution of highly localized positive-energy states of the free Dirac electron

Highly localized positive-energy states of the free Dirac electron are constructed and shown to evolve in a simple way under the action of Dirac's equation. When the initial uncertainty in position is small on the scale of the Compton wavelength, there is an associated uncertainty in the mean energy that is large compared with the rest mass of the electron. However, this does not lead to any breakdown of the one-particle description, associated with the possibility of pair-production, but rather leads to a rapid expansion of the probability density outwards from the point of localization, at speeds close to the speed of light.

Scalable Visualization of Galaxies, Oceans, and Brains

One of the challenges in scientific visualization is to generate software libraries suitable for the large-scale data emerging from tera-scale simulations and instruments. We describe the efforts currently under way at SDSC and NPACI to address these challenges. The scope of the SDSC project spans data handling, graphics, visualization, and scientific application domains. Components of the research focus on the following areas: intelligent data storage, layout and handling, using an associated “Floor-Plan” (meta data); performance optimization on parallel architectures; extension of SDSC’s scalable, parallel, direct volume renderer to allow perspective viewing; and interactive rendering of fractional images (“imagelets”), which facilitates the examination of large datasets. These concepts are coordinated within a data-visualization pipeline, which operates on component data blocks sized to fit within the available computing resources. A key feature of the scheme is that the meta data, which tag the data blocks, can be propagated and applied consistently. This is possible at the disk level, in distributing the computations across parallel processors; in “imagelet” composition; and in feature tagging. The work reflects the emerging challenges and opportunities presented by the ongoing progress in high-performance computing (HPC) and the deployment of the data, computational, and visualization Grids.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Probability backflow for a Dirac particle

The phenomenon of probability backflow, previously quantified for a free nonrelativistic particle, is considered for a free particle obeying Dirac's equation. It is known that probability backflow can occur in the opposite direction to the momentum; that is to say, there exist positive-energy states in which the particle certainly has a positive momentum in a given direction, but for which the component of the probability flux vector in that direction is negative. It is shown thar the maximum possible amount of probability that can flow backwards, over a given time interval of duration T, depends on the dimensionless parameter epsilon = root 4h/mc(2)T, where m is the mass of the particle and c is the speed of light. At epsilon = 0, the nonrelativistic value of approximately 0.039 for this maximum is recovered. Numerical studies suggest that the maximum decreases monotonically as epsilon increases from 0, and show that it depends on the size of m, h, and T, unlike the nonrelativistic case.

The relationship between plasma lactate parameters, W-peak and 1-h cycling performance in women

Purpose: The relationship between six descriptors of lactate increase, peak (V) over dot O-2,W-peak, and 1-h cycling performance were compared in 24 trained, female cyclists (peak (V) over dot O-2 = 48.11 +/- 6.32 mL . kg(-1) . min(-1)). Methods: The six descriptors of lactate increase were: 1) lactate threshold (LT; the power output at which plasma lactate concentration begins to increase above the resting level during an incremental exercise test), 2) LT1 (the power output at which plasma lactate increases by 1 mM or more), 3) LTD (the lactate threshold calculated by the D-max method), 4) LTMOD (the lactate threshold calculated by a modified D-max method), 5) L4 (the power output at which plasma lactate reaches a concentration of 4 mmol-L-1), and 6) LTLOG (the power output at which plasma lactate concentration begins to increase when the log([La-]) is plotted against the log (power output)). Subjects first completed a peak (V) over dot O-2 test on a cycle ergometer. Finger-tip capillary blood was sampled within 30 s of the end of each 3-min stage for analysis of plasma lactate. Endurance performance was assessed 7 d later using a 1-h cycle test (OHT) in which subjects were directed to achieve the highest possible average power output. Results: The mean power output (W) for the OHT (+/- SD) was 183.01 +/- 18.88, and for each lactate variable was: LT (138.54 +/- 46.61), LT1 (179.17 +/- 27.25), LTLOG (143.97 +/- 45.74), L4 (198.09 +/- 33.84), LTD (178.79 +/- 24.07), LTMOD (212.28 +/- 31.75). Average power output during the OHT was more strongly correlated with all plasma lactate parameters (0.61 < r < 0.84) and W-peak (r = 0.81) than with peak (V) over dot O-2 (r = 0.55). The six lactate parameters were strongly correlated with each other (0.54 < r < 0.91) and of the six lactate parameters, LTD correlated best with endurance performance (r = 0.84). Conclusions: It was concluded that plasma lactate parameters and W-peak provide better indices of endurance performance than peak (V) over dot O-2 and that, of the six descriptors of lactate increase measured in this study, LTD is most strongly related to 1-h cycling performance in trained, female cyclists.

Eigenvalues of Casimir operators for gl(m/infinity)

A full set of Casimir operators for the Lie superalgebra gl(m/infinity) is constructed and shown to be well defined in the category O-FS generated by the highest-weight irreducible representations with only a finite number of non-zero weight components. The eigenvalues of these Casimir operators are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(m/infinity) are also determined.

Thermal and radiation curing of phenylethynyl terminated macromers

The thermal and gamma-irradiation induced curing of two phenylethynyl terminated composite resin systems, DFB/BPF and PETI5A, was investigated. Thermal curing of these matrix resin samples was performed at a temperature of 360 degrees C, gamma irradiation of the samples was conducted at 300 degrees C at a dose rate of 2.2 kGy h(-1). The reaction and subsequent loss of ethynyl groups in the resins for both cure methods was demonstrated by observing the decrease of the 2215 cm(-1) peak in the Raman spectra of the resins. Fully cured resin samples were found to have glass transition temperatures of 244-246 degrees C and 278-280 degrees C for DFB/BPF and PETI5A respectively. Similar relationships between T-g and fractional conversion were observed in both resins. The apparent polymerization rate, R-p, for thermal cure at 360 degrees C, was found to be 4.79 x 10(-2)% s(-1) in PETI5A and 3.22 x 10(-2)% s(-1) in DFB/BPF. Catastrophic degradation under nitrogen was observed to commence near 450 degrees C and 530 degrees C, with 5% weight losses occurring at 455 degrees C and 540 degrees C for DFB/BPF and PETI5A respectively. Gamma radiation induced cure at 300 degrees C was shown to be feasible, with full cure being reached with doses of 40 kGy for DFB/BPF and 100 kGy for PETI5A.

Risk management for scuba diving operators on Australia's Great Barrier Reef

Australia's Great Barrier Reef is one of the world's most popular scuba diving destinations. Unfortunately, a series of recent diving injuries and deaths has tarnished the region's safety record. In particular, media attention surrounding the disappearance of American divers Thomas and Eileen Lonergan has focused attention on dive operators' legal responsibilities and the consequences of failing to discharge their duty of care to customers. This paper briefly examines the relevant Australian law for recreational diving operations, and reviews risk management strategies that may reduce or prevent the occurrence of future problems. (C) 2000 Elsevier Science Ltd. All rights reserved.

Level-one highest weight representation of U-q[sl((N)over-cap vertical bar 1)] and Bosonization of the multicomponent Super t-J model

We study the level-one irreducible highest weight representations of the quantum affine superalgebra U-q[sl((N) over cap\1)], and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible U-q[sl((N) over cap\1)] modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multicomponent super t-J model by using the bosonized vertex operators. (C) 2000 American Institute of Physics. [S0022- 2488(00)00508-9].

Coupled experimental and thermodynamic modeling studies for metallurgical smelting and coal combustion slag systems

An extensive research program focused on the characterization of various metallurgical complex smelting and coal combustion slags is being undertaken. The research combines both experimental and thermodynamic modeling studies. The approach is illustrated by work on the PbO-ZnO-Al2O3-FeO-Fe2O3-CaO-SiO2 system. Experimental measurements of the liquidus and solidus have been undertaken under oxidizing and reducing conditions using equilibration, quenching, and electron probe X-ray microanalysis. The experimental program has been planned so as to obtain data for thermodynamic model development as well as for pseudo-ternary Liquidus diagrams that can be used directly by process operators. Thermodynamic modeling has been carried out using the computer system FACT, which contains thermodynamic databases with over 5000 compounds and evaluated solution models. The FACT package is used for the calculation of multiphase equilibria in multicomponent systems of industrial interest. A modified quasi-chemical solution model is used for the liquid slag phase. New optimizations have been carried out, which significantly improve the accuracy of the thermodynamic models for lead/zinc smelting and coal combustion processes. Examples of experimentally determined and calculated liquidus diagrams are presented. These examples provide information of direct relevance to various metallurgical smelting and coal combustion processes.